The foundation of mathematics, formalizing collections of objects (sets), their elements, and membership relations.
founder:: Georg Cantor
axiomatization:: ZFC (Zermelo-Fraenkel with Choice)
core concepts:: set, element, subset, union, intersection, complement, power set
cardinality measures the size of a set, distinguishing countable from uncountable infinities
The diagonal argument proves the reals are uncountable, establishing a hierarchy of infinities
Provides the language for logic, topology, algebra, category theory, and probability
Russell's paradox motivated axiomatic approaches replacing naive set theory
Related:: number theory, combinatorics, graph theory, information theory